It is known to use internal-to-vehicle mechanisms for monitoring the air pressure of the tires of a vehicle. These mechanisms have a stationary device which interacts with a device that co-moves with the respective wheel of the vehicle in such a way that monitoring of the air pressure can take place during operation of the vehicle. The co-moving device uses suitable means to sense the air pressure, and transmits an output-related signal to the stationary device if the air pressure falls below a certain value. A prerequisite for operation of these systems is that the co-moving device have an energy supply, for example a small battery rotating along with the wheel being monitored. This configuration must therefore be included in ongoing maintenance cycles so that a battery exchange is performed at the proper time. The battery exchange leads to additional costs. Moreover, the mass of the rotating wheel is influenced by the requisite battery device; in particular, an asymmetrical mass distribution results, which requires additional counterweights. Overall wheel balance is therefore degraded.